Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include<iostream>
#include<algorithm>

using namespace std;

int main() {
  int N;
  cin >> N;
  int a[N];
  for(int i = 0; i < N; i++) {
    cin >> a[i];
  }
  sort(a,a+N);
  double Max = 0;
  for(int i = 0; i < N-1; i++) {
    int tmp1 = a[i+1] - a[i];
    int tmp2 = 0;
    if(i == N - 2) {
      tmp2 = a[i-1] + a[i-2];
    } else if(i == N - 3) {
      tmp2 = a[N-1] + a[i-1];
    } else {
      tmp2 = a[N-1] + a[N-2];
    }
    Max = max((double)tmp2 / tmp1,Max);
  }
  printf("%.10lf\n",Max);
}